Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities

Abstract

In this paper, we give converses of the Jensen and Edmundson-Lah-Ribarič inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function. As an application, we also derive improved converse relations for generalized means, for the Hölder and Hermite-Hadamard inequalities as well as for the inequalities of Giaccardi and Petrović.